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Virial theorem for rotating self-gravitating Brownian particles and two-dimensional point vortices

We derive the proper form of Virial theorem for a system of rotating self-gravitating Brownian particles. We show that, in the two-dimensional case, it takes a very simple form that can be used to obtain general results about the dynamics of the system without being required to solve the Smoluchowski-Poisson system explicitly. We also develop the analogy between self-gravitating systems and two-dimensional point vortices and derive a Virial-like relation for the vortex system.

preprint2009arXivOpen access
Pierre-Henri Chavanis
cond-mat.stat-mech
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Pierre-Henri Chavanis

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